Multiply the following complex numbers: $({5+i}) \cdot ({2+4i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5+i}) \cdot ({2+4i}) = $ $ ({5} \cdot {2}) + ({5} \cdot {4}i) + ({1}i \cdot {2}) + ({1}i \cdot {4}i) $ Then simplify the terms: $ (10) + (20i) + (2i) + (4 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 10 + (20 + 2)i + 4i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 10 + (20 + 2)i - 4 $ The result is simplified: $ (10 - 4) + (22i) = 6+22i $